University of Groningen
Unintended Consequences of Central Bank Lending in Financial Crises
van der Kwaak, Christiaan
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1
2020011-EEF
Unintended Consequences of Central Bank
Lending in Financial Crises
July 2020
Christiaan van der Kwaak
2
SOM is the research institute of the Faculty of Economics & Business at the University of Groningen. SOM has six programmes:
- Economics, Econometrics and Finance - Global Economics & Management - Innovation & Organization
- Marketing
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3
Uninteded Consequences of Central Bank Lending in
Financial Crises
Christiaan van der Kwaak
University of Groningen, Faculty of Economics and Business, Department of Economics, Econometrics and Finance
Unintended Consequences of Central Bank
Lending in Financial Crises
∗
Christiaan van der Kwaak
†July 6, 2020
Abstract
I investigate the effectiveness of central bank lending to undercapitalized financial in-termediaries in mitigating the macroeconomic impact of financial crises. I show that the requirement to pledge collateral has a contractionary effect on private credit everything else equal when central banks provide more funding for one euro of government bonds than for one euro of private credit. I apply the model to the Italian economy during the time of the ECB’s three-year Longer-Term Refinancing Operations (LTROs), and show that this collateral effect can explain why Italian banks’ private credit grew by only 2% while their holdings of domestic government bonds grew by 30%. Finally, I find that the three-year LTROs contained an implicit subsidy to the Italian banking system of 140 basis points.
Keywords: ‘Financial Intermediation; Macrofinancial Fragility; Unconventional Monetary Policy’
JEL: E32, E44, E52, G21
∗The first draft of this paper (2015) circulated under the title “Financial Fragility and Unconventional Central
Bank Lending Operations”. I acknowledge the generous support of the Dutch Organization for Sciences, through the NWO Research Talent Grant No. 406-13-063. I am grateful to Sweder van Wijnbergen, Wouter den Haan, Nicola Gennaioli, Jose Victor Rios-Rull, Ricardo Reis, Franklin Allen, Ethan Ilzetzki, Lukas Schmid, Thomas Eisenbach, Toni Ahnert, Christian Stoltenberg, Bjoern Bruggeman, Petr Sedlacek, Omar Rachedi, Anatoli Segura, Nuno Palma, Agnese Leonello, Enrico Mallucci, Alex Clymo, Patrick Tuijp, Oana Furtuna, Damiaan Chen, Lucyna Gornicka and Egle Jakucionyte, as well as seminar participants at the University of Manchester, the University of Kent, the National Bank of Hungary, the University of Groningen, Bank of Lithuania, the University of Amsterdam, and the Tinbergen Institute for helpful comments and suggestions.
†Affiliation: Rijksuniversiteit Groningen. Address: Nettelbosje 2, 9747 AE Groningen. Email address:
1
Introduction
In this paper I investigate the effectiveness of central bank lending to undercapitalized financial intermediaries in mitigating the macroeconomic impact of financial crises. I show that the requirement to pledge collateral gives rise to a collateral effect that has a contractionary impact on the macroeconomy, everything else equal, and thereby reduces the expansionary effect that such lending otherwise has. This effect arises because central banks typically provide more funding for one euro of government bonds than for one euro of private credit. Consequently, the possibility to borrow from the central bank can induce intermediaries to reduce private credit to create additional space for government bonds when they have limited balance sheet capacity in a financial crisis. I apply the framework developed in this paper to the unconventional three-year LTROs of December 2011 and February 2012 under which the Italian banking system borrowed AC181.5 billion from the European Central Bank (ECB). The collateral effect explains why Italian banks’ private credit only grew by 2% (relative to no intervention (Carpinelli and Crosignani, 2018)), while their holdings of domestic sovereign debt increased by 30%. While this paper’s focus is on the three-year LTROs, my framework could also be relevant for studying the macroeconomic impact of other central banks’ lending programs, such as the Federal Reserve’s Term Auction Facility and the Treasury Securities Lending Facility.
I first analyze a two-period general equilibrium model incorporating leverage-constrained financial intermediaries that are partially financed through central bank funding. This model allows me to analytically establish the collateral effect and to identify the deep parameters that determine the relative strength of the collateral effect with respect to the expansionary effect that such lending also has (Gertler and Kiyotaki, 2010; Bocola, 2016; Engler and Große Steffen, 2016; Cahn et al., 2017). To demonstrate the empirical relevance, I construct a New Keynesian DSGE model with financial frictions which I estimate with the help of Bayesian techniques and a moment-matching exercise using Italian data.
I capture the fact that Italian banks were undercapitalized since the Great Financial Crisis (International Monetary Fund, 2011; Hoshi and Kashyap, 2015) by employing the Gertler and Karadi (2011) framework, in which an incentive compatibility constraint limits the size of inter-mediaries’ balance sheet by the amount of net worth. I extend this framework in two directions. First, financial intermediaries have a portfolio choice between government bonds, reserves and corporate securities, the last of which is used by non-financial corporations to finance produc-tive ‘physical’ capital (Gertler and Karadi, 2013; Van der Kwaak and Van Wijnbergen, 2014; Kirchner and van Wijnbergen, 2016; Bocola, 2016). Second, I introduce collateralized central bank lending, which represents an alternative form of funding in addition to net worth and de-posits. Intermediaries have to pledge collateral to obtain central bank funding, for which both government bonds and corporate securities can be used. However, one euro of government bonds provides more funding than one euro of corporate securities. The central bank supplies any amount of funding as long as sufficient collateral is pledged. I argue in Section 2 that the three-year LTROs contained an implicit subsidy to Italian banks with respect to the ECB’s regular
short-term funding. I capture this implicit subsidy by temporarily decreasing the interest rate on central bank funding with respect to that on reserves (Engler and Große Steffen, 2016), both of which are set by the central bank. I investigate the policy both within a closed economy and a small open economy that is a member of a currency union; these economies capture the two extremes in terms of the influence that Italian macrodevelopments have on the Italian policy rate, which is set by the ECB and based on macrodevelopments in the Eurozone as a whole.1
The main contribution of this paper is the identification of the collateral effect, and the key parameters that determine its strength. I show how this effect reduces or offsets the expansion-ary effect that central bank lending to intermediaries has on the macroeconomy in other New Keynesian models with financial frictions (Gertler and Kiyotaki, 2010; Bocola, 2016; Engler and Große Steffen, 2016; Cahn et al., 2017). The modeling innovation that gives rise to this effect is the combination of i) balance-sheet-constrained financial intermediaries that are subject to ii) differential collateral requirements when obtaining central bank funding. A second contri-bution is that the collateral effect explains the accumulation of domestic government bonds by Southern-European commercial banks following the announcement of the three-year LTROs as documented in Crosignani et al. (forthcoming) and Section 2, while simultaneously explaining the limited growth of Italian private credit by 2% (relative to no intervention, Carpinelli and Crosignani (2018)). A third contribution is to provide an estimate of the implicit subsidy to Italian commercial banks that was contained in the three-year LTROs, which I find to be equal to 140 annual basis points.
A final contribution is that my model provides an explanation for the empirical finding of Carpinelli and Crosignani (2018) that the maturity of the three-year LTROs of December 2011 and February 2012 was a key feature for these operations to have an expansionary effect on credit provision to the real economy: the longer financial intermediaries can profit from lower funding costs, the larger the increase in the expected discounted sum of future profits, and the larger the relaxation of their incentive compatibility constraints. While the collateral effect still induces a relative shift from corporate credit to government bonds, the longer maturity creates sufficient balance sheet space for financial intermediaries to simultaneously expand the level of credit provision to the real economy.
Related literature
In this literature review I limit myself to the papers closest related to my paper. A more elaborate review can be found in Appendix A.
Drechsler et al. (2016), Carpinelli and Crosignani (2018), Garcia-Posada and Marchetti 1Italian macrodevelopments affect the policy rate one for one in a closed economy, while they do not affect
the policy rate at all in a small open economy that is a member of a currency union. In reality, Italy comprises approximately 15% of Eurozone GDP, implying that Italian macrodevelopments will affect the policy rate of the ECB. However, their influence will be much smaller than that in a closed-economy model.
(2016), and Andrade et al. (2019) study the ECB’s unconventional LTROs at the level of indi-vidual banks. Drechsler et al. (2016) focus on the role of the ECB as a Lender of Last Resort (LOLR) during the European sovereign debt crisis. They find that weakly capitalized banks bor-rowed more from the ECB, pledged riskier collateral, and actively invested the funds borbor-rowed from the ECB in distressed sovereign debt after the start of the European sovereign debt crisis in 2010. Their sample, however, does not include the three-year LTRO of February 2012.
Carpinelli and Crosignani (2018), Garcia-Posada and Marchetti (2016), and Andrade et al. (2019) specifically focus on the three-year LTROs, and find a positive effect on credit provision to the real economy in Italy, Spain, and France, respectively. In addition, Andrade et al. (2019) find that three-year LTROs expand loan supply by more than shorter-maturity LTROs.
Other mechanisms that explain why banks were accumulating government bonds during the European sovereign debt crisis are moral suasion (Altavilla et al., 2017; Becker and Ivashina, 2018; Ongena et al., 2019) and risk-shifting (Acharya and Steffen, 2015; Drechsler et al., 2016; Crosignani, 2016; Acharya et al., 2018). These papers also find that such an accumulation of government bonds reduced credit provision to the real economy. A second reason why credit provision to the real economy was reduced during the sovereign debt crisis was capital losses on impaired sovereign bond holdings on bank balance sheets (Popov and Horen, 2015; Altavilla et al., 2017; Acharya et al., 2018).
My paper also relates to Gertler and Kiyotaki (2010); Gertler and Karadi (2011, 2013), who study the transmission to the macroeconomy of shocks to the balance sheets of financial intermediaries. The key property of these papers is that the size of intermediaries’ balance sheets is limited by the amount of net worth through an endogenous leverage constraint.
A key result of this paper is that there is crowding out of credit provision to the real economy by government bonds through the collateral effect. Other theoretical papers that feature crowding out are Kirchner and van Wijnbergen (2016) and Crosignani (2016), where it is caused by a debt-financed fiscal expansion increasing commercial banks’ bond holdings (Kirchner and van Wijnbergen, 2016), and risk shifting (Crosignani, 2016). Other reasons for a reduction in credit provision to the real economy are capital losses on government bonds that reduce intermediaries’ net worth through the so-called bank-sovereign nexus (Van der Kwaak and Van Wijnbergen, 2014; Bocola, 2016).
My paper is also related to the Lender of Last Resort (LOLR) literature, of which Bagehot (1873) was the first to argue that central banks should lent freely against good collateral at high rates. In order for banks to take out central bank funding during a financial crisis, LOLR funding must be subsidized in some way relative to funding sources in private markets: otherwise LOLR lending would offer no benefit over the private market, and banks would not borrow from it. I capture this implicit subsidy by temporarily reducing the interest rate on central bank funding relative to that on deposit funding, in line with Engler and Große Steffen (2016).
The more recent literature that investigates the effects from central bank lending within the standard DSGE framework can broadly speaking be distinguished between collateralized and
uncollateralized lending. One of the first papers to explicitly model uncollateralized central bank lending is Gertler and Kiyotaki (2010). Bocola (2016) and Cahn et al. (2017) extend this framework to investigate the impact of the ECB’s unconventional LTROs. These papers do not feature a collateral requirement, and therefore miss the contractionary collateral effect. As a result, LTROs only have an expansionary effect on bank lending and output because central bank lending directly relaxes intermediaries’ incentive compatibility constraint.
A second strand of literature features a collateral requirement to obtain central bank funding, but the agents who borrow from the central bank are not balance-sheet-constrained (Schabert, 2015; H¨ormann and Schabert, 2015; Engler and Große Steffen, 2016). As a result, these agents can perfectly elastically acquire additional collateral in case central bank funding becomes more attractive. This contrasts with my paper, where the combination of collateral requirements and endogenous leverage constraints causes a tradeoff to emerge between acquiring additional government bonds (which provide the most central bank funding per euro) and credit provision to the real economy.
I describe some stylized facts in section 2. The two-period model is analyzed in section 3, while the infinite-horizon model description can be found in section 4, while section 5 discusses the calibration and estimation procedure. Section 6 presents the results from my simulations, while section 7 discusses the results and evaluates several robustness checks. Finally, section 8 concludes the paper.
2
Stylized facts
In this section I present some stylized facts regarding the aggregated balance sheets of Monetary Financial Institutions (MFIs) from Italy, Portugal and Spain at the time of the three-year LTROs. I do so for two reasons. First, I show that the three-year LTROs induced MFIs from these countries to purchase large amounts of domestic government bonds. Second, I argue that the three-year LTROs contained an implicit subsidy for MFIs from the above countries.
Data from the refinancing operations of the ECB were collected from Bruegel (2015), while balance sheet data of MFIs were collected from the ECB’s statistical warehouse (European Cen-tral Bank, 2015).2 The time series have a monthly frequency. Balance sheet data of MFIs,
excluding the European System of Central Banks, are available at a country level.3 The vast
majority of euro-area MFIs are credit institutions (i.e., commercial banks, savings banks, post-banks, specialized credit institutions, among others) (European Central Bank, 2011b).
Figure 1 shows domestic government bond holdings as a percentage of total assets of Monetary Financial Institutions (MFIs) excluding the European System of Central Banks in Italy, Spain, 2The ECB refers to its lending operations as ‘refinancing operations’. In this section I will follow the ECB’s
terminology.
3MFIs include “credit institutions and non-credit institutions (mainly money market funds) whose business
is to receive deposits from entities other than MFIs and to grant credit and/or invest in securities” (European Central Bank, 2011b).
and Portugal. From the figure we see a clear increase in domestic government bondholdings of one to one-and-a-half percentage points of total MFI assets for all three countries during the period in which the three-year LTROs took place. The increase in holdings of domestic government bonds is also large in absolute levels, amounting to a striking 30% measured in euros see Appendix H. Finally, there is a clear break in the holdings of domestic government bonds around the time of the three-year LTROs, which make it plausible that this increase can be attributed to the three-year LTROs. These results are in line with the findings of Carpinelli and Crosignani (2018) and Crosignani et al. (forthcoming).
01/01/20113 01/01/2012 01/01/2013 4 5 6 7 8 9
Dom. government bonds (% of MFI assets) IT
ES PT
Figure 1: Domestic government bond holdings as a percentage of total assets of Monetary Finan-cial Institutions (MFIs) excluding the European System of Central Banks in Italy (IT), Spain (ES), and Portugal (PT) from January 2011 to January 2013. The two dashed vertical lines refer to December 1st, 2011 and March 1st, 2012, respectively, which mark the beginning and the end of the period in which the two LTROs took place, respectively. Source: ECB.
Figure 2 shows the stock of total refinancing operations at the ECB, as well as the country use by MFIs in Italy, Spain and Portugal. Total refinancing operations consist of the sum of main refinancing operations (MROs) and all longer-term refinancing operations (LTROs). MROs are one-week liquidity providing operations in euro, while regular LTROs are three-month liquidity providing operations.4
Figure 2 suggests three main observations. First, the stock of total refinancing operations increased by more than 40% fromAC800 billion to approximatelyAC1150 billion during the period in which the three-year LTROs took place.
Second, a disproportionate share of the funding went to MFIs in Italy, Spain and Portugal. By March 1st, 2012, more than 50% of total ECB funding had been borrowed by MFIs from these countries, while their cumulative share in Eurozone GDP is less than one-third. Apparently, the
Country use of ECB funding 01/01/20110 01/01/2012 01/01/2013 200 400 600 800 1000 1200 1400
Total Refinancing Operations (EUR billion) IT
ES PT RE
Figure 2: Country use of the stock of total refinancing operations, consisting of the sum of of outstanding MROs and LTROs, by MFIs in Italy (IT), Spain (ES), Portugal (PT) and the rest of the Eurozone (RE) in AC billion from January 2011 to January 2013. The two vertical lines refer to December 1st, 2011 and March 1st, 2012, which mark the beginning of the period in which the three-year LTROs took place and the end, respectively. Source: Bruegel (2015).
three-year LTROs of December 2011 and February 2012 were especially attractive for MFIs in Italy, Spain and Portugal.
Third, the use of ECB funding by MFIs from these three countries amounted to a large share of their respective GDP. On March 1st, 2012, ECB funding accounted forAC181.5 billion andAC400 billion of debt funding for Italian and Spanish MFIs, respectively, amounting to approximately 10% of Italian GDP and 40% of Spanish GDP, respectively.
The above observations suggest that the three-year LTROs were an attractive source of funding for MFIs from Italy, Spain and Portugal, as they borrowed significant amounts from the ECB. This raises the question whether there might have been a subsidy element that made these LTROs particularly attractive. At first sight, however, one would argue that this is not the case; the interest rate was ‘fixed at the average rate of the main refinancing operations over the life of the respective operation’ (European Central Bank, 2011a). As a result, there was no difference in terms of funding costs between a strategy where MFIs borrowed at the ECB at a three-year maturity, and a strategy where they borrowed at a weekly maturity, and roll over for three years (Carpinelli and Crosignani, 2018). Therefore, there was no direct subsidy from the ECB to the MFIs that participated in the three-year LTROs. However, there are two reasons why it can be argued that these unconventional LTROs contained an implicit subsidy.
First, after the bankruptcy of Lehman Brothers in September 2008 the ECB started to provide a so-called ‘haircut subsidy’ on risky securities such as distressed sovereign debt from the above-mentioned countries (Drechsler et al., 2016). A haircut is the difference between the value of the
collateral pledged and the amount of funding received. The haircut subsidy entailed the ECB offering haircuts that were below private-market haircuts, thereby providing more funding for the same amount of collateral. Without any implicit subsidy, MFIs from Italy, Spain and Portugal would have been indifferent between private market funding and ECB funding, and would not have borrowed from the ECB (Drechsler et al., 2016).
Second, there was uncertainty whether MFIs would be able to continue to roll over MRO funding, as the fixed-rate full allotment policy under which this was possible was supposed to be a temporary measure.5 The three-year LTROs eliminated this uncertainty, and was therefore
more attractive than the ECB’s regular MROs, despite the fact that the cumulative interest payments would be the same under the two strategies (Carpinelli and Crosignani, 2018).
For these two reasons I argue that the three-year LTROs contained an implicit subsidy to MFIs from Italy, Spain and Portugal. This was different for MFIs from countries such as Germany and the Netherlands, whose domestic bonds were not subject to a haircut subsidy, and who took out relatively little ECB funding over this period, as private market funding offered equally or more attractive sources of funding (Carpinelli and Crosignani, 2018).
3
Analytical results within a two period model
In this section I develop a two-period model to analyse the key mechanisms that affect lending by undercapitalized financial intermediaries to the real economy when the central bank provides them with low-interest-rate funding. In particular, I show that such a policy can potentially have a contractionary effect on lending, despite lowering funding costs for financial intermediaries. In addition, I investigate the way in which deep parameters affect lending decisions to prepare for the quantitative analysis in Section 6.
3.1
Model setup
The economy contains periods t = 0 and t = 1 and is populated by households, production firms, financial intermediaries, and a government. The government consists of a fiscal authority and a central bank, which sets the interest rate on central bank reserves and on loans to financial intermediaries. Financial intermediaries have access to unlimited amounts of central bank fund-ing, provided that they pledge sufficient government bonds as collateral. In addition, they are financed by household deposits and net worth. Assets consist of corporate loans to production firms, government bonds and central bank reserves, presenting intermediaries with a portfolio choice similar to Gertler and Karadi (2013), and Bocola (2016). Intermediaries are subject to an incentive compatibility constraint as in Gertler and Karadi (2011), which prevents them from perfectly elastically expanding the balance sheet in case of arbitrage opportunities. Households 5The fixed-rate full allotment policy consisted of the ECB providing as much funding as demanded by MFIs
as long as sufficient collateral was pledged. This policy was introduced in October 2008 in response to the Great Financial Crisis, and was supposed to be temporary. However, it is still in place today.
choose in period t = 0 between consumption and saving through deposits and government bonds, which are subject to quadratic transaction costs when their bond holdings deviate from the tar-get level. Income in period t = 1 is consumed after lump sum taxes have been paid to the fiscal authority. Households have a standard utility function that is concave in consumption. Produc-tion firms borrow from financial intermediaries in period t = 0 to purchase physical capital in a perfectly competitive market, and use this capital to produce goods in period t = 1 using a production function that is concave in physical capital. After paying intermediaries the marginal product of capital in period t = 1, the remaining profits are transferred to households. The fiscal authority enters period t = 0 with outstanding long-term bonds that are held by households and financial intermediaries. No revenues or expenditures are raised in period t = 0, and hence the stock of long-term bonds at the end of period t = 0 is equal to that at the beginning of period t = 0. At the beginning of period t = 1, the fiscal authority receives central bank profits, and raises lump sum taxes on households to repay bondholders.
3.1.1 Central bank
Central bank reserves mR0 enter the economy through lending dcb0 to financial intermediaries. I
assume the central bank has zero net worth in period t = 0. Therefore, the central bank balance sheet is given by dcb
0 = mR0. To obtain central bank funding, intermediaries have to pledge
government bonds qb0sb0as collateral:
dcb0 ≤ θbqb 0s
b
0. (1)
where 0 ≤ θb < 1 is set by the central bank, and determines how much central bank funding is obtained for one euro of government bonds.6 Intermediaries remain the legal owner of the
bonds, and receive the accompanying cash flows after repayment of the central bank loan in period t = 1.
The central bank sets the interest rate rR
0 on central bank reserves mR0 and the interest rate
rcb
0 on central bank funding to intermediaries dcb0. In line with the ECB’s fixed rate full allotment
policy, the central bank provides any amount of central bank funding (full allotment) as long as sufficient government bonds are pledged as collateral.7 Central bank profits in period t = 1 are transferred to the fiscal authority.
I argued in Section 2 that the three-year LTROs contained an implicit subsidy which I capture by decreasing the interest rate on central bank funding with respect to that on reserves, which will turn out to be equal to the interest rate on deposits in equilibrium. As a result, central 6In reality, commercial banks can also pledge other assets as collateral, such as corporate bonds, covered bonds,
and certain types of corporate loans. The central bank, however, typically provides less liquidity for one euro of those assets than for one euro of government bonds. To simplify the analysis and be able to obtain closed-form analytical expressions, I omit the possibility to pledge corporate loans as collateral in this section, as the key objective is to disentangle the different mechanisms that influence credit provision to the real economy. However, intermediaries will be able to pledge corporate loans in the infinite-horizon DSGE model in subsequent sections, in which it turns out that the qualitative results from this section carry over as long as one euro of corporate loans provides less liquidity than one euro of government bonds.
bank funding becomes a more attractive source of funding than deposit funding (Engler and Große Steffen, 2016).
3.1.2 Financial intermediaries
Financial intermediaries enter period t = 0 with net worth n0. They attract deposits d0 from
households, and obtain funding dcb
0 from the central bank to purchase government bonds sb0 at a
price q0b, finance loans sk0 to production firms, and keep reserves mR0 at the central bank: sk0+ q0bsb0+ mR0 = n0+ d0+ dcb0 . (2)
As discussed above, the central bank requires intermediaries to pledge government bonds qb 0sb0
as collateral. Loans sk
0 and government bonds qb0sb0 pay a net return r0k and r0b in period t = 1
respectively, while reserves earn an interest rate r0R. Intermediaries pay a net interest r0d on deposits and rcb
0 on central bank funding. Therefore, net worth n1 in period t = 1 is given by:
n1= 1 + r0k s k 0+ 1 + r b 0 q b 0s b 0+ 1 + r R 0 m R 0 − 1 + r d 0 d0− 1 + rcb0 d cb 0. (3)
Intermediaries are interested in maximizing expected discounted net worth E0[βΛ0,1n1], where
βΛ0,1 denotes the households’ stochastic discount factor, as households are the ultimate owners
of financial intermediaries. However, intermediaries face an incentive compatibility constraint as in Gertler and Karadi (2011) that arises from the possibility to costlessly divert a fraction λa of
asset a ∈ {a = k, b} at the end of period t = 0.8,9Depositors, however, anticipate this possibility,
and will in equilibrium only provide deposits up to the point where the continuation value of the intermediary is larger than or equal to the benefits from diverting assets:
E0[βΛ0,1n1] ≥ λksk0+ λbq0bs b
0. (4)
The optimization problem of intermediaries is given by maximizing E0[βΛ0,1n1] subject to (1)
- (4). In Appendix B, I derive the first order conditions, and show that the interest rate on central bank reserves rR
0 equals the interest rate on deposits r0d, as financial intermediaries can
perfectly elastically attract additional deposits to increase reserves. Next, I consider the first order condition that pins down the portfolio choice between corporate loans and government bonds: λb λk E0βΛ0,1 rk0− r d 0 = E0βΛ0,1 r0b− r d 0 + θ bE 0βΛ0,1 rd0− r cb 0 | {z } Collateral value of gov’t bonds , (5) 8Note that λ
adoes not refer to legal risk weights as in the Basel III regulations. Instead, this is a requirement
imposed by one group of private agents (depositors) on another group of private agents (financial intermediaries), rather than a requirement imposed by the government.
9As central bank reserves are electronic accounts administered by the central bank, I assume that it is impossible
Throughout my analysis, I assume that rd
0 ≥ rcb0 . Otherwise, intermediaries would not use any
central bank funding, as deposit funding would have lower costs while not requiring intermediaries to pledge collateral.10 The first two terms are familiar from Gertler and Karadi (2013). The left
hand side denotes the marginal cost from reducing corporate loans by one euro, as expected net worth decreases by rk0− rd
0 everything else equal. This wedge between the return on corporate
loans and deposits exists because of the binding incentive compatibility constraint (4). Similarly, the first term on the right hand side denotes an increase in expected net worth from increasing government bonds by one euro. However, the first order condition contains an additional term relative to Gertler and Karadi (2013) which captures the collateral value that government bonds provide: an additional euro of government bonds provides θb euros of central bank funding,
which reduces intermediaries’ funding costs when rcb
0 < rd0, and thereby raises their expected net
worth everything else equal. As such, we see that the possibility to pledge government bonds as collateral shifts intermediaries’ portfolio choice from corporate loans to government bonds everything else equal.
In addition, observe that the collateral value increases with the interest rate difference rd 0−rcb0 :
in that case an additional euro of government bonds decreases funding costs by more, and intermediaries will therefore want to increase their stock of government bonds. Finally, central bank lending will not affect intermediaries’ portfolio decisions when rd
0 = r0cb. In that case,
intermediaries are indifferent between deposit funding and central bank funding. As a result, the collateral value of government bonds is zero, and intermediaries’ portfolio choice between corporate loans and government bonds is only determined by the expected return differences between corporate loans and government bonds on the one hand, and deposits on the other.
Next, I employ the intermediaries’ first order conditions in Appendix B, together with the law of motion for net worth (3), to rewrite the incentive compatibility constraint (4) in the following way:
(1 + µ0) n0≥ λksk0+ λbq0bs b
0, (6)
where µ0 denotes the multiplier on the incentive compatibility constraint (4). This (in)equality
says that the weighted sum of loans sk0 and government bonds q0bsb0 is limited by the amount of
net worth n0 when constraint (6) is binding. In that case, equality (6) can be interpreted as
the intermediary being undercapitalized, which is the relevant case in this paper, since European commercial banks have been undercapitalized since the financial crisis of 2007-2009 (International Monetary Fund, 2011; Hoshi and Kashyap, 2015). Finally, I assume that intermediaries carry over bond holdings sb−1 that were acquired in period t = −1, as commercial banks in Southern-Europe already had large holdings of domestic government bonds before the announcement of the three-year LTROs. As a result, net worth n0 depends on the bond price in period t = 0:
n0 = nex0 + qb0sb−1, (7)
10Another reason for assuming rd
0 ≥ rcb0 which does not feature in my model but is relevant for the real world
is the fact that credit risk on unsecured funding is larger than on secured funding, and therefore carries a higher interest rate, everything else equal.
where nex
0 does not depend upon decisions taken in period t = 0. Therefore, an increase in the
bond price qb0relaxes intermediaries’ incentive compatibility constraint (6) everything else equal,
and allows them to expand their balance sheet.
3.2
Analysis of a decrease in central bank funding costs
The main goal of this section is to investigate the short-run effect on credit provision to the real economy of a policy under which the interest rate on central bank funding rcb
0 is reduced while
keeping the interest rate on reserves rR
0 constant, a policy which I will refer to as LTRO-policy. I
focus on credit provision to the real economy, as this is the key transmission mechanism through which the three-year LTROs should have affected the Eurozone economy. A second goal is to determine which deep parameters are driving the short-run impact of the LTRO-policy to inform my estimation procedure for the full infinite-horizon model in subsequent sections.
To enhance the analysis, I introduce the variable Γcb
0, which is the difference between the
interest rate on reserves rR
0 and central bank funding rcb0 . Since the interest rates on reserves
and deposits are equal in equilibrium, see Section 3.1.2, a decrease of the interest rate on central bank funding will reduce funding costs relative to deposit funding Γcb
0 ≡ rR0−rcb0 = r0d−r0cb(Engler
and Große Steffen, 2016). There are no other shocks, therefore my analysis is deterministic. I start the analysis by differentiating the incentive compatibility constraint (6), the first order condition for intermediaries’ portfolio choice between corporate loans and government bond (5), and the market clearing condition for government bonds with respect to Γcb
0. I subsequently
substitute the last two expressions into the first to obtain the following results, the details of which can be found in Appendix B.
Proposition 1. The bond price qb
0 always increases in response to an increase in Γcb0 , i.e. dqb
0 dΓcb
0
> 0.
Proof of Proposition 1. See Appendix B.
The intuition is the following: an increase in Γcb
0 induces intermediaries to shift from deposit
funding to central bank funding. As they need to pledge additional government bonds as collat-eral, the demand for bonds increases while the supply is unchanged. Therefore, the bond price has to increase to clear the market. This result is in line with the observed drop in Southern-European bond yields around the time of the three-year LTROs, as yields move inversely with bond prices (Crosignani et al., forthcoming; Krishnamurthy et al., 2018).
Having established that bond prices will always increase, we can immediately see that inter-mediaries’ net worth n0 will always increase as a result of the LTRO-policy:
Proposition 2. Net worth n0 always increases in response to an increase in Γcb0, i.e. dΓdncb0 0
> 0.
Proof of Proposition 2. Differentiation of equation (7) gives the following derivative: dn0 dΓcb 0
=
sb−1· dq0b
Hence the LTRO-policy always increases intermediaries’ net worth n0 as a result of capital
gains on intermediaries’ existing bond holdings. Therefore, the policy relaxes intermediaries’ incentive compatibility constraints everything else equal, which allows them to expand their balance sheets, for example by expanding credit provision to the real economy. Indeed, such an indirect recapitalization of the financial sector was found to have an empirically relevant effect on credit supply in the context of the ECB’s Outright Monetary Transactions (OMT) program (Acharya et al., 2019).
Interestingly, we see in Proposition 3 that such an indirect recapitalization does not necessarily expand credit provision to the real economy, and can even have a contractionary effect on credit provision:
Proposition 3. The impact of a marginal increase in Γcb
0 on credit provision to the real economy
is ambiguous, i.e. dsk0 dΓcb
0 ≶ 0.
Proof of Proposition 3. Differentiation of the incentive compatibility constraint (6) with respect to Γcb
0, and subsequent substition of Proposition 2 and the differentiated market clearing condition
for government bonds gives the following expression for lending to the real ecnomy:
dsk 0 dΓcb 0 = 1 λk− Cn0 (1 + µ0) sb−1 | {z } capital gains effect − λb sb0+ q b 0 κsb,h | {z } collateral effect · dq b 0 dΓcb 0 , (8)
where C < 0, and κsb,h > 0 the coefficient in front of the quadratic adjustment costs facing
households when purchasing government bonds. The sign of (8) is ambiguous, since the collateral effect and the capital gains effect have opposite signs. Details can be found in Appendix B.
Besides the above-mentioned capital gains effect, we see the emergence of a collateral effect that reduces credit provision to the real economy everything else equal: the shift from deposit funding to central bank funding forces intermediaries to purchase additional government bonds to be pledged as collateral. As a result, the market value of intermediaries’ holdings of government bonds increases because of higher bond prices (first term of the collateral effect) and additional bonds purchased from households (second term of the collateral effect). As the size of their balance sheets is limited by the amount of net worth, lending to the real economy sk0 decreases
everything else equal. Interestingly, we see from expression (8) that the net effect of the LTRO-policy on credit provision to the real economy can be negative if the collateral effect dominates the capital gains effect. This suggests that the policy could be counterproductive in improving short run macroeconomic conditions.
Note from equation (8) that the collateral effect is eliminated when λb = 0, in which case
intermediaries can expand their holdings of government bonds without tightening the incentive compatibility constraint (6). Alternatively, if existing bond holdings sb
will not incur any capital gains on existing bond holdings while there is crowding out of lending to the real economy when acquiring additional government bonds. In that case, the LTRO-policy is always contractionary when λb> 0.
In addition to disentangling the capital gains effect and the collateral effect, the analysis also shows the crucial role of the coefficient governing households’ transaction costs κsb,h in
determining the strength of the collateral effect. To see how this parameter affects the collateral effect, I take the partial derivative of (8), which captures the direct effect of a change in κsb,h.
Proposition 4. The direct effect from a marginal increase in κsb,h raises lending to the real
economy: ∂κ∂ sb,h dsk 0 dΓcb 0 > 0.
Proof of Proposition 4. See Appendix B.
An increase in κsb,h raises households’ marginal cost from changing their holdings of
gov-ernment bonds, which makes them less willing to sell govgov-ernment bonds everything else equal. Therefore, intermediaries will be able to buy fewer bonds in equilibrium, which reduces the strength of the collateral effect. At the same time, bond prices have to increase by more to achieve market clearing, which strengthens the capital gains effect. Therefore, lending to the real economy will increase in equilibrium.
To sum up: I show that the LTRO-policy has an ambiguous effect on lending by financial intermediaries to the real economy, which is the key transmission mechanism through which the LTRO-policy can affect macroeconomic conditions. I disentangle an expansionary capital gains effect and a contractionary collateral effect. This contractionary effect arises because intermedi-aries need to acquire additional government bonds to pledge as collateral. The possibility that the general equilibrium effect on credit provision to the real economy can be contractionary rather than expansionary sharply contrasts with the existing DSGE literature, in which central bank discount window lending always has an expansionary effect (Gertler and Kiyotaki, 2010; Bocola, 2016; Engler and Große Steffen, 2016; Cahn et al., 2017). In addition, the collateral effect has the potential to explain why Italian banks only invested AC22.6 billion out of AC181.5 billion in three-year LTRO funding in private credit, while they invested almost four times this amount (AC82.7 billion) in Italian government bonds (Carpinelli and Crosignani, 2018).
To quantitatively investigate whether this is the case, I will extend the current model to an infinite-horizon DSGE model that I estimate on Italian data. From my analysis we see that κsb,h will be an important parameter in the estimation procedure, as it is a key parameter in
determining the strength of the collateral effect. In line with the collateral policy of the ECB I will also allow corporate loans to be pledged as collateral. While this will obviously reduce the strength of the collateral effect, it will not eliminate it, as central banks typically provide more funding for one euro of government bonds than for one euro of private loans.
4
Infinite-horizon DSGE model
In this section I extend the two-period model to an infinite-horizon DSGE model to quantitatively assess the strength of the collateral effect and the extent to which the three-year LTROs were capable of improving macroeconomic conditions in Italy. Specifically, I employ a standard closed economy New Keynesian model, and check in Appendix E.2 that the results carry over to a model version of a small open economy that is a member of a currency union. I do so to check that my results do not depend on the way conventional monetary policy is modeled; these model versions capture the two extremes in terms of the influence that Italian macrodevelopments have on the Italian policy rate. One extreme is that they affect the policy rate one-for-one in the closed economy, while the other extreme is that they have zero influence on the policy rate in the small open economy model. In reality, the Italian policy rate is set by the ECB, which bases its policy decisions on macrodevelopments in the Eurozone as a whole. With the Italian economy comprising around 15% of Eurozone GDP, the influence of Italian macrodevelopments will be somehwere in between that in the closed economy and the small open economy model.
The structure of the financial sector is the same as in the two-period model and again subject to the Gertler and Karadi (2011) incentive compatibility constraint. However, intermediaries can also pledge corporate securities as collateral, but obtain less central bank funding than for one euro of government bonds. The central bank sets the nominal rather than the real interest rate on central bank funding and reserves, the last of which follows an active Taylor rule.
Households maximize the sum of expected discounted utility with habit formation in con-sumption to more realistically capture concon-sumption dynamics (Christiano et al., 2005). They save through deposits, corporate securities, and government bonds, the last two of which are subject to quadratic adjustment costs (Gertler and Karadi, 2013). Wages are sticky, as house-holds’ wage and labor decisions are modeled as in Erceg et al. (2000). Households receive profits from ownership of all firms in the economy, and pay lump sum taxes to the government. The government honors outstanding obligations and purchases final goods. These expenditures are financed from central bank dividends, lump-sum taxes and issuance of (long-term) debt.
Intermediate goods producers borrow from financial intermediaries to purchase physical cap-ital from capcap-ital goods producers that are subject to convex adjustment costs. Final labor and physical capital are then used for the production of the intermediate goods, which are sold to retail goods producers who face monopolistic competition and sticky price adjustments as in Calvo (1983). Final goods producers purchase retail goods to produce a final good that is sold in a perfectly competitive market. The final good is used by households for consumption, by capital goods producers for investment, by the government, and for adjustment costs arising from households’ transactions in financial markets. A full exposition of the model can be found in Appendix C.1.
Finally, I do not include sovereign default risk in the main text, despite the fact that Italy was in the middle of a sovereign debt crisis at the time of the three-year LTROs. Instead, I report in Appendix E.1 a model version which includes endogenous sovereign default risk, and
check that my results from the main text continue to hold.
4.1
Government
4.1.1 Fiscal authority
The government has three sources of revenue: debt issue qb
tbt, lump sum taxes τt, and dividends
from the central bank ∆cbt . These revenues are used to pay for (exogenous) government purchases of the final good gtand service outstanding government liabilities 1 + rtb qbt−1bt−1. Therefore,
the period t government budget constraint (in terms of the price level of the final good Pt) is
given by:
qbtbt+ τt+ ∆cbt = gt+ 1 + rbt q b
t−1bt−1. (9)
Government debt is long-term, and its maturity structure follows Woodford (1998, 2001). These bonds pay a cash flow xcthat is decaying at a rate 1−ρ per period. Hence ρ effectively determines
the maturity structure of the bonds. In Appendix C.4.1 I formally show that the real rate of return rb
t on a bond issued in period t − 1 is given by:
1 + rbt = xc+ (1 − ρ) qtb / πtqt−1b , (10)
where πt≡ Pt/Pt−1denotes the gross inflation rate of the final good. Finally, lump sum taxes
τt are given by a rule which ensures the intertemporal government budget constraint is satisfied
(Bohn, 1998). A more elaborate description of the fiscal authority can be found in Appendix C.4.1.
4.1.2 Central Bank
The central bank sets the nominal interest rate rtn,r on reserves mR
t by employing a standard
Taylor-rule that satisfies the Taylor-principle. Reserves are created when the central bank pro-vides funding dcb
t to financial intermediaries. However, unlike Section 3, I assume that part of
the central bank’s assets are financed by net worth ncb
t .11 In that case, the central bank’s balance
sheet constraint (in terms of the price level of the final good Pt) is given by:
dcbt = ncbt + mRt, (11)
Financial intermediaries have to pledge collateral in the form of corporate securities and govern-ment bonds to obtain central bank funding. The central bank provides θta eurocents in funding
for one euro of collateral from asset class a = {k, b}. Intermediaries remain the legal owner of the assets they pledge as collateral, and therefore receive the accompanying cash flows after
repayment of the central bank loan in period t + 1.12 The collateral constraint has the following functional form: dcbj,t≤ θk tq k ts k,p j,t + θ b tq b ts b,p j,t. (12)
where the central bank is in charge of the haircut parameters θkt and θtb, which I assume to be
constant over time. Just as in Section 3 the central bank provides as much funding as demanded by financial intermediaries (full allotment), provided they pledge sufficient collateral. The central bank receives a nominal interest rate rtn,cbon loans dcb
t to financial intermediaries. Pre-dividend
net worth ncb∗
t (in terms of the price level Ptof the final good) is the difference between the gross
return on loans dcbt−1provided to financial intermediaries in period t − 1, and the gross return on
reserves mR t−1issued in period t − 1: ncb∗t = 1 + r n,cb t−1 πt ! dcbt−1− 1 + r n,r t−1 πt mRt−1= 1 + rcbt dcb t−1− (1 + r r t) m R t−1, (13) where rr
t and rcbt denote the net real return on reserves and central bank funding, respectively.
A fraction δcb
t of ncb∗t is paid out to the fiscal authority, while the remaining funds are retained
by the central bank:
∆cbt = δtcbncb∗t , (14)
ncbt = 1 − δcbt ncb∗t , (15)
where I assume δcb
t to be constant over time.13 In addition to the nominal interest rate on
reserves, the central bank also controls the nominal interest rate rtn,cb on central bank funding by adjusting the spread Γcbt :
rtn,cb= rn,rt − Γcb
t , with Γ cb
t = ¯Γcb+ κcb cbt− ¯cb + κξ ξt− ¯ξ , (16)
where ¯Γcb is the steady state spread. cbt and ξt follow lognormal AR(1) processes, with ξt
representing the quality of capital, a negative shock of which triggers financial crises as in Gertler and Karadi (2011). Just as in Section 3 the LTRO-policy will be captured through an increase in Γcb
t , and the equilibrium interest rate on reserves will be equal to that on deposits. Therefore,
an increase in Γcbt will also decrease the interest rate on central bank funding with respect to
that on deposits.
12Financial intermediaries are not subject to limited liability in the Gertler and Karadi (2011) framework, and
will therefore always repay their creditors. In addition, I calibrate the model in such a way that intermediaries never have negative net worth in equilibrium.
13Central banks typically operate with positive net worth, and pay part of their profits as dividends to the fiscal
authority. To ensure that both features are incorporated, I set 0 < δcb
t < 1. Note that this implies that the fiscal
authority (partially) recapitalizes the central bank when pre-dividend net worth ncb∗
4.2
Financial intermediaries
Financial intermediaries purchase corporate securities sk,pj,t that are issued by intermediate goods producers at a price qkt, and government bonds s
b,p
j,t at a price q b
t. In addition, they hold reserves
mR
j,t at the central bank. They fund their assets through net worth nj,t, risk-free household
deposits dj,tand central bank funding dcbj,t, for which they need to pledge collateral, see equation
(12). Total assets pj,t are given by:
pj,t= qkts k,p j,t + q b ts b,p j,t + m R j,t= nj,t+ dj,t+ dcbj,t, (17)
Net worth in period t + 1 is the difference between the return on assets and the return on liabilities: nj,t+1= 1 + rkt+1 q k ts k,p j,t + 1 + r b t+1 q b ts b,p j,t + 1 + r R t+1 m R j,t− 1 + r d t+1 dj,t− 1 + rt+1cb d cb j,t, (18)
where rkt is the net real return on corporate securities in period t, rtb the net real return on
government bonds, rR
t the net real return on central bank reserves, rtd the net real return on
deposits and rcb
t the net real return on central bank funding. Following Gertler and Karadi
(2011), intermediaries are forced to shut down with probability σ, which is i.i.d. and exogenous, both in time and the cross-section. Intermediaries that are forced to stop operating pay out all remaining net worth to their respective household, the ultimate owner of the intermediary. As long as they continue operating, intermediaries maximize their continuation value, which is the sum of expected future discounted profits:
V sk,pj,t−1, sb,pj,t−1, mRj,t−1, dj,t−1, dcbj,t−1 = max Et n βΛt,t+1 h (1 − σ) nj,t+1+ σV sk,pj,t, sb,pj,t, mRj,t, dj,t, dcbj,t io ,
where βΛt,t+1denotes households’ stochastic discount factor. A similar agency problem between
depositors and managers of intermediaries arises as in Section 3 (Gertler and Karadi, 2011):
V sk,pj,t−1, sb,pj,t−1, mRj,t−1, dj,t−1, dcbj,t−1 ≥ λkqkts k,p j,t + λbqtbs b,p j,t, (19)
which I assume to be binding throughout my simulations as the Italian banking system was undercapitalized at the time of the three-year LTROs (International Monetary Fund, 2011; Hoshi and Kashyap, 2015). The optimization problem of intermediary j is given by maximizing Vsk,pj,t−1, sb,pj,t−1, mR
j,t−1, dj,t−1, dcbj,t−1
subject to the balance sheet constraint (17), the collateral constraint(12), the law of motion for net worth (18), and the incentive compatibility constraint (19).
The resulting first order conditions are derived in Appendix C.2. Just as in Section 3, I find that the equilibrium interest rate on reserves and deposits is the same, as intermediaries can perfectly elastically obtain reserves by attracting additional deposits to arbitrage away any
(ex-pected) return difference between reserves and deposits. Intermediaries’ portfolio choice between corporate securities and government bonds is given by a very similar expression as equation (5) for the two-period model:
λb λk EtΩt,t+1 rkt+1− r d t+1 = EtΩt,t+1 rbt+1− r d t+1+ θbt− λb λk θkt EtΩt,t+1 rdt+1− r cb t+1 , (20) where Ωt,t+1 = βΛt,t+1[(1 − σ) + σχt+1] is the intermediary’s stochastic discount factor with
χt the Lagrangian multiplier on the intermediary’s balance sheet constraint (17). This discount
factor can be interpreted as the household’s stochastic discount factor βΛt,t+1, augmented by an
additional term to incorporate the effect of the financial frictions. Again, the second term on the right hand side denotes the collateral effect. Observe, however, that the strength of the collateral effect is reduced, everything else equal, because of the presence of the term (λb/λk) θkt: there is
less need to shift from corporate securities to government bonds now that corporate securities also provide intermediaries with central bank funding.
Two other features from the two-period model carry directly over to the infinite-horizon ver-sion of the model. First, central bank lending will not affect intermediaries’ portfolio deciver-sions when rd
t = rcbt as the collateral value of assets becomes zero in that case. Second, the
incen-tive compatibility constraint effecincen-tively limits the size of intermediaries’ holdings of corporate securities and government bonds by the amount of net worth similar to equation (6):14
χtnj,t= λkqkts k,p
j,t + λbqbts b,p
j,t, (21)
Finally, a fraction 1 − σ of intermediaries is forced to stop operating at the beginning of each period. They are replaced by new intermediaries which are provided with a starting net worth equal to a fraction χb of previous period net worth of the old intermediary.
4.3
Production sector
The production sector is modeled in standard New Keynesian fashion. I will shortly outline the setup below, with a more detailed exposition in Appendix C.3. There is a continuum i ∈ [0, 1] of intermediate goods producers that operate in a perfectly competitive market. They issue corporate securities at the end of period t − 1 and use the proceeds to purchase physical capital ki,t−1 from capital producers at a price qt−1k . As in Gertler and Kiyotaki (2010), intermediate
goods producers can credibly pledge all after-wage revenues from period t to the buyers of these securities. Shocks are realized at the beginning of period t, among which a capital quality shock that transforms capital ki,t−1 into ξtki,t−1 effective units of capital (Gertler and Karadi, 2011).
Next, intermediate goods producers hire labor hi,t in a perfectly competitive market from labor
14Note that λk
t and λbt do not represent the legal capital requirements from Basel III (according to which λbt
should be equal to zero), but capture an agency problem between two groups of private agents (namely depositors and financial intermediaries). Such an interpretation is consistent with λb
t > 0, which will be the case in my
agencies at a wage rate wt, and start producing intermediate goods with a
constant-returns-to-scale production function with effective capital ξtki,t−1 and labor hi,t as inputs, and capital
income share α. Output yi,t is sold to retail firms at a price mt, while the effective capital stock
(after depreciation δ per effective unit of capital) is sold to capital producers at a price qk
t. As the
remaining after-wage revenues are paid out to corporate securities’ holders, I get the following expression for the net return rk
t on these securities: 1 + rkt =αmtyi,t/ki,t−1+ q k t (1 − δ) ξt qk t−1 . (22)
As in Gertler and Karadi (2011), the capital quality shock ξtdecreases the return on corporate
securities rtk for two reasons. First, output yi,t decreases as capital becomes less productive,
thereby reducing the first term of (22). Second, the capital price qk
t will fall in the presence of a
binding incentive compatibility constraint (21), thereby reducing the second term in (22). Capital producers purchase the after-production capital stock (1 − δ) ξtkt−1 from
intermedi-ate goods producers at price qk
t, and convert it one-for-one into new capital. In addition, they
purchase final goods to produce additional capital. However, the conversion from final goods to capital goods is subject to quadratic adjustment costs. As a result, one unit of investment typically results in less than one unit of capital goods. The newly produced capital stock is sold to intermediate goods producers at a price qk
t.
A continuum of retail firms transforms intermediate goods one-for-one into differentiated retail goods. Retail firms operate in a monopolistic competitive market, and are therefore price-setters that charge a markup over the input price mt. Following Calvo (1983), each retail firm
faces a probability ψp that they cannot choose a new price in the current period. In that case,
they can partially index with previous period inflation. Final good producers purchase goods from all retail firms to produce a final good with a CES production function, and sell in a perfectly competitive market.
4.4
Market clearing & equilibrium
In equilibrium, the total number of corporate securities ktmust equal the total number of
secu-rities purchased by households and financial intermediaries. Similarly, the total supply of bonds must equal the number of bonds purchased by households and financial intermediaries:
kt = sk,ht + s k,p t , (23) bt = sb,ht + s b,p t . (24)
The aggregate resource constraint is given by:
yt = ct+ it+ gt+ 1 2κsk,h sk,ht − ˆsk,h 2 +1 2κsb,h sb,ht − ˆsb,h 2 , (25)
where the last two terms represent the quadratic adjustment costs paid by households when purchasing corporate securities and government bonds (Gertler and Karadi, 2013). The resulting equilibrium definition can be found in Appendix D, which gives a complete overview of the first order conditions.
5
Calibration & estimation
I employ a mix of calibration and estimation with both Bayesian methods and moment matching to match the Italian economy as close as possible. To do so, I employ data downloaded from Eurostat, the ECB, and the Italian National Institute for Statistics, a description of which can be found in Appendix F.
I break the identification of parameter values into four stages. In the first two stages I employ a model version without financial frictions and central bank lending operations, while I employ the full model in the last two stages. Specifically, I partially calibrate my model in the first stage by either taking parameter values that are standard in the macroeconomic literature or targeting first order moments such as the steady state labor supply. I subsequently estimate the remaining parameters in the second stage by employing Bayesian techniques. I calibrate some of the parameters relating to financial frictions in the third stage, and estimate the remaining parameters in the fourth stage through a second-order moment matching exercise on data from the financial crisis period 2008Q1-2011Q4.
Specifically, I employ the following quarterly time series from the period 1999Q1-2007Q4 in my Bayesian estimation: real GDP per capita, real consumption per capita, real investment per capita, hours worked, inflation, and the three-month nominal interest rate. Unlike many papers in the literature (Bocola, 2016; Cahn et al., 2017; Darracq-Pari`es and K¨uhl, 2017; K¨uhl, 2018), I specifically perform the Bayesian estimation on a model version without financial frictions and central bank lending operations. Such a model version accurately captures the pre-2008 economic environment for several reasons. First, there was no implicit subsidy to the Italian banking sys-tem pre-2008 (Drechsler et al., 2016), which is in my model captured by rn,rt = rn,cbt .15 In that
case the collateral value of intermediaries’ assets is equal to zero (equation (20)), and hence inter-mediaries’ choice between corporate securities and government bonds is not affected by central bank lending operations. Second, financial frictions were likely to be absent or negligible during the 1999Q1-2007Q4 period, which is in my model captured by intermediaries’ incentive com-patibility constraints (19) being non-binding. Under those conditions the equilibrium allocation coincides exactly with that in a model version without financial frictions. The choice to estimate a model version without financial frictions is further supported by Del Negro et al. (2016), who 15Before October 2008 the interest rate on reserves was (approximately) equal to the interest rate at which
MFIs borrowed from the ECB; ECB liquidity would be auctioned to Eurozone MFIs, allowing the interest rate on the ECB loans to be slightly higher than the interest rate on required reserves (MRO-rate). In October 2008 the ECB switched to a fixed rate full allotment procedure, under which Eurozone MFIs can borrow at the MRO-rate (European Central Bank, 2011b). The last case exactly corresponds with rn,rt = r
n,cb
show that estimated models with financial frictions perform worse during normal times than models without those frictions.16
To save space, I will only discuss the calibration/estimation of key parameters, and refer the interested reader to Appendix G for more information on how the remaining parameters are chosen, as well as tables with calibrated and estimated parameter values.
Two key parameters that determine the strength of the collateral effect are θtjwith j ∈ {k, b}. While the ECB does not publish the haircut 1 − θjt it applies to different asset types, Bruegel
(2018) replicates them using long-term credit ratings. Bruegel (2018) finds that the haircut on Italian government bonds was between 3 and 7% during the sovereign debt crisis of 2011-2013. I therefore set θb
t = 0.95. Next, I set θkt = 0.40, which implies a haircut of 60% on corporate
securities. Although most assets that can be pledged as collateral at the ECB have haircuts that are significantly smaller, my model setup does not distinguish between private assets that are eligible as collateral and those that are not, for which the ECB provides zero euros in liquidity.17
Therefore, the 60% haircut can be interpreted as the average haircut on a portfolio that contains both pledgeable and non-pledgeable private assets.
We remember from Section 3 that λb and κsb,h are the key parameters that determine the
strength of the collateral effect. I determine the ratio λb/λk by comparing the average spread
between the return on corporate securities and deposits with the average spread between the Italian bond yield and the return on deposits.18 Next, I employ a moment-matching exercise to the full model with binding financial constraints (19) to pin down κsb,h and the quadratic
adjustment costs for corporate securities κsk,h.
19 The moment-matching exercise targets the
standard errors of real GDP per capita, real consumption per capita, real investment per capita, and the credit spread between the expected return on corporate securities and deposits over the period 2008Q1-2011Q4. Ideally, I would have estimated these two parameters in the Bayesian estimation procedure of the model version without financial frictions to ensure consistency be-tween the models with and without financial frictions. However, the Bayesian estimation would not converge for this model version. Therefore, I take the point estimates from the moment-matching exercise, and redo the Bayesian estimation on a model version that includes quadratic adjustment costs to check that the parameter estimates from the original Bayesian estimation are not biased. More details on this specific issue can be found in Appendix G.3.
Finally, I pin down the size of the implicit subsidy of the three-year LTROs (captured by the increase in Γcb
t in response to a financial crisis) by matching the net uptake of ECB funding by
16Bocola (2016) estimates a model version with financial constraints that are occassionaly binding by solving
the model using global solution methods and estimating it by using particle filters. Unlike Bocola (2016), my model has too many state variables to employ such a strategy.
17For example, in 2010 haircuts varied from 1.5% for investment grade corporate bonds with a maturity less
than one year to 64.5% for non-investment grade credit claims with a maturity of more than 10 years, see also https://www.ecb.europa.eu/press/pr/date/2010/html/sp090728 1annex.en.pdf.
18I can write equation (20) as λb
λk =
¯ rb−¯rd ¯
rk−¯rd in the non-stochastic steady state, since the second term on the
right hand side is equal to zero because ¯Γcb= ¯rn− ¯rn,cb= 0. 19Although κ
sk,h did not feature in the analysis of Section 3, one can argue along similar lines as for κsb,h that
the aggregate Italian commercial banking system over the period in which the unconventional LTROs of December 2011 and February 2012 took place. I find the implicit subsidy to be equal to annual 140 basis points, or equivalently 35 quarterly basis points, something I will discuss more elaborately in Sections 6.4 and 7.
6
Results
In this section I show the results from numerical simulations of my model, which I solve by performing a first order perturbation around the deterministic steady state. As mentioned above, I will model the LTRO-policy by (temporarily) reducing the nominal interest rate on central bank funding relative to that on reserves, in line with Engler and Große Steffen (2016).
I set the stage by showing the results to a regular central bank funding shock cbt, see equation
(16), which allows me to highlight the key mechanisms that are operative under the LTRO-policy. I follow up on the two-period model analysis by investigating how the impulse response functions change when varying key parameters that determine the strength of the collateral effect, such as the collateral requirements θk
t and θtb, and the household transaction costs parameter κsb,h.
Next I look at a scenario where the LTRO-policy is employed in the middle of a financial crisis to properly capture the fact that the three-year LTROs took place in the middle of a financial crisis. This crisis is initiated through a negative capital quality shock as in Gertler and Karadi (2011). I distinguish between a limited LTRO-policy in which the interest rate spread between the nominal interest rate on reserves and central bank funding Γcb
t follows the capital quality
shock (and reverts back to the steady state following a regular AR(1)-process), and three-year LTROs in which Γcb
t is increased for 12 quarters, after which Γcbt immediately returns to steady
state. This allows me to highlight the influence of the maturity of the program on credit provision and the macroeconomy.
6.1
A regular central bank funding shock
I start by investigating the regular central bank funding shock cbt in equation (16). This shock
reduces the nominal interest rate on central bank funding by 35 basis points with respect to the nominal interest rate on reserves on impact, after which it reverts back to steady state, see panel “Interest rate difference” in Figure 3. Let us first focus on the blue solid line, which denotes the base case, and defer discussion of the red slotted line to the next section. This simulation will allow me to identify the key mechanisms of the model, and set the stage for subsequent sections in which I look at the interaction of this policy with financial crises.
Figure 3 shows that a reduction of the interest rate on central bank funding relative to that on deposit funding has a positive effect on the macroeconomy: financial intermediaries expand lending to the real economy (see panel “Corporate securities (b)”), and investment and output increase.
